1 Introduction

1.1 Background

The physical and/or operational damage from the heat and/or residual smoke in the aftermath of a fire in a building is largely a safety/engineering determination. Additionally, once the immediate toxic gases and particulates have dissipated, residual combustion deposits on surfaces may pose potential airborne and/or dermal exposure hazards to cleanup and response personnel which should be factored into site cleanup and restoration [1,2,3,4,5]. However, evaluating and defining building “damage” due to combustion residual from smoke at increasing peripheral distances from the fire origin to delineate the boundaries of impact, is also of concern. This latter assessment task is less straightforward, and cleanup/restoration based upon such an evaluation may be as costly and disruptive as for the areas that sustained direct and obvious damage. The primary criterion by which to assess post fire conditions and extent of impact are based upon visual inspection and/or the presence of characteristic “smoke” odor [6,7,8,9,10,11,12,13]. Environmental testing for combustion residual on surfaces is frequently conducted to supplement visual inspection and may also be implemented to help clarify related issues such as (but not limited to) determination of impact from possibly different sources, delineate scope of cleanup/restoration, or identification and documenting of acceptably “clean” conditions following cleanup prior to re occupancy.

The smoke emitted from a fire is a combination of particles, aerosols and gases (which can condense as solids). The nature and relative number of various constituents of smoke are driven primarily by the materials burned/consumed as fuel, as well as the conditions (e.g., availability of oxygen) at the location/origin of the fire. Much of the guidance literature regarding assessment and post fire environmental remediation in buildings is directed toward wildfires as an exterior smoke/pollutant source, given the widespread environmental and resulting economic impacts. However, primary assessment and testing protocols for building structural fires as discussed herein largely overlap.

1.2 Summary of Combustion Residual Analytical Approaches and Limitations

Terminology relating to combustion particulate and other concepts relevant to assessment of post fire conditions have not been systematically codified, and reflect the constituent engineering, construction, forensic, air pollution, laboratory analysis and public health disciplines that may be involved in a given circumstance [4, 14,15,16,17,18]. Smoke particles from a fire are frequently described relative to the characteristics of carbon black, which is defined in ASTM International (ASTM) D6602 Standard Practice for Sampling and Testing of Possible Carbon Black Fugitive Emissions or Other Environmental Particulate or Both. [19, 20]. Carbon black consists of an engineered commercial product with designed particle size that exists as an aggregated aciniform (“grapelike”) structure. Soot is defined in D6602 as a submicron (less than one [1] micrometer; μm) black powder produced as an extraneous by product of combustion (i.e., fire), as detected under high magnification via transmission electron microscopy (TEM). Soot from an uncontrolled fire is generated at relatively lower temperatures and accordingly contains significant amounts of adsorbed organic tars and volatile compounds. The large soot aggregates and clusters that result from gas phase partitioning and settling onto other particles and surfaces range from 1 μm to 100 μm, and are visible and quantifiable via light microscopy. In addition, depositional patterns can often be used to differentiate impact indicative of a fire from other background combustion sources. Char which is also generated from a fire, is defined as a particulate larger than one (1) μm, and may contain some of the original (fuel) material’s structure or components observable via light microscopy. As with soot, char may also have various adsorbed volatile and semi-volatile organic components, some of which are carcinogens, and many of which generate the characteristic unpleasant post-fire acrid odors.

Building materials such as wood and synthetics that are consumed in typical oxygen limited conditions that occur in structural fires, will produce greater quantities of soot that is typically more diagnostic for differentiating indoor (i.e. structural fire) from outdoor (i.e., wildfire) origin [9, 10, 20]. Ash, which is typically a combustion byproduct in wildfires and much less so in structural fires, is a grey mineralized particulate in which most if not all of the carbon has been oxidized with little of the original organic components remaining. (Ash is not specifically defined in D6602 but rather is incorporated as a component of the particulates reported as char).

Analytically, D6602 prescribes a screening test, by which particles with the aciniform morphology suggestive of soot are distinguished from char (and ash) in surface samples. Sampling is conducted most frequently (but not exclusively) by extracting surface dust via either a clear “sticky” tape (subsequently mounted onto a glass slide) or an engineered flexible plastic slide coated with an adhesive. (Collectively, both are referred to as media for “tape sampling”). Analysis is then conducted using a variety of light microscopy techniques. Automobile/truck exhaust, wood stoves/indoor cooking, tire wear particulates, industrial emissions and many other sources contribute to the ubiquitous presence of soot and char particles as “background” [21,22,23,24]. Thus, mere detection of soot and/or char via light microscopy on surfaces following a fire may not be definitive in attributing conditions (beyond obvious physical damage and/or discoloration) to a specific fire event. Under D6602, scanning and/or transmission electron microscopy (SEM/TEM) with energy dispersive X-ray analysis (EDS) is also employed for high resolution images as well as to delineate particle chemistry for confirmation of carbon content and other markers that may be potentially useful for inferring origins(s) and/or source(s) of the fire. However, tape samples are incompatible with TEM analysis, which requires collection via wipe sampling. In conjunction with the actual sample preparation and analytical procedure, the potential for obscuring and/or altering the structure and deposition patterns of any collected combustion particulates limits strict application of TEM via ASTM D6602 to post fire investigations as described herein [25].

Similar analytical methods to the light microscopy delineated in ASTM D6602 are described in ANSI Standard IESO/RIA 6001 Evaluation of Heating Ventilation and Air Conditioning (HVAC) Interior Surfaces to Determine the Presence of Fire-Related Particulate as a Result of a Fire in a Structure, and the Technical Guide for Wildfire Impact Assessments for the OEHS Professionals published by the American Industrial Hygiene Association (AIHA) [26, 27]. As with D6602, IESO/RIA 6001 and the AIHA Technical Guide employ light microscopy to detect the presence of soot and char particles as indicators of fire impact. However, both IESO/RIA 6001 and the AIHA Technical Guide also identify the necessity for dark field reflected light capability to enable discrimination of “burned” from “unburned” particles based upon surface color and reflectivity. Unlike D6602, IESO/RIA 6001 protocol also prescribes analysis of a wipe sample collected in conjunction with a sticky tape sample that reveals no char or soot greater than 1 μm; electron microscopy is optional. Ultimately ASTM D6602, IESO/RIA 6001 as well as the AIHA Wildfire Guide depend upon light microscopy for identification and semi quantification of char and soot, and collectively represent the analysis for much of environmental particulate data generated in post fire building assessment to determine smoke impact.

1.3 The Quantification Problem

There are varying perspectives regarding the purpose of post fire surface sampling, which in turn dictates the form in which data may be reported and ultimately evaluated. Accumulating evidence to identify a suspected source of settled particulate has its genesis in industrial quality control such as clean room manufacturing. In this instance, the mere detection of a unique and specific “marker” contaminant or assemblage of contaminants can be associated with a given source or process such as mechanical wear [17, 28,29,30]. For wildfires, the generated smoke will likely contain char and ash with discernible characteristics via light microscopy that can be associated with specific plant life and/or soils known to have been consumed as fuel or affected by the heat of the wildfire [17, 31]. Because tape sampling extracts settled particulate while maintaining the original deposition layers and particle orientation, assemblage analysis, while not specified in ASTM D6602 or IESO/RIA 6001, can nevertheless be informative. In the case of structural fires, the identification and difference(s) in spatial distribution of soot across zone(s) relative to the combustion sources(s) as an index of impact, is often of greater interest and will be the focus here.

Light microscopy analysis can report soot (and char) concentration as percent ratio, or surface loading as particle count per surface area (counts/cm2 or counts/mm2). Both are currently used interchangeably. Percent ratio is often (but not exclusively) determined by visual area estimation (VAE) in which the analyst estimates the sample area observed in the microscope covered by the particulate of interest through comparison with standardized reference charts. VAE has historically been useful as a rapid method for estimating relative mineral composition in rock specimens where such information was relevant to geological/petrological research and/or related engineering purposes [32,33,34]. Similarly, VAE has also been incorporated into the industrial hygiene/indoor environmental quality disciplines for estimating the asbestos content for samples of building materials and insulation products as required for regulatory compliance. As adapted for post fire soot assessment, VAE reports the percentage of soot aggregates as the midpoint of the estimated range of the area of soot relative to other particulates observed [19, 33]. Alternatively, some laboratories may perform actual soot particle counting and report concentration as percent ratio of soot particles relative to the total number of particles counted. A refinement of this latter approach that may be utilized involves factoring in the average soot aggregate particle size in each reporting category to calculate the relative percent value [17, 35].

Reporting soot loading as counts/cm2 or counts/mm2 parallels quantification and sampling data for other frequently encountered surface contaminants such as lead (micrograms/ft2) and asbestos (fibers/cm2). Unlike percent ratio which is a relative metric dependent on the presence of other extraneous particulates, surface loading provides a semi quantification of the actual amount of soot present [17]. Ultimately as a result of the lack of fixed numerical standards for soot (and char) particulates as either surface loading or concentration, comparative sampling is recommended to characterize surface conditions in areas suspected to have been impacted to varying degrees relative to other relevant building space(s) of interest. The latter include, for example, spaces either assumed (or so hypothesized) to be representative of background conditions [36,37,38]. This ultimately provides a basis for inference regarding extent and/or origin of smoke/soot impact (within the analytical limitations of the method) under the premise that surface deposition is dependent upon distance from the fire’s origin [39].

1.4 Case Example

An agricultural research/educational facility in the southwest United States sustained a small smoldering fire in a first-floor battery storage room within the four-story main building of the campus. In addition to the heavy smoke damage in the battery room and immediately adjoining/adjacent spaces (subsequently identified as Phase I), smoke permeated throughout the surrounding occupied areas of the main building. Preliminary post fire evaluation of the battery storage room and Phase I spaces resulted in concerns for more widespread impact. These additional areas included various functional spaces in the main building (collectively identified as Phase II) as well as a basement utility connector and a large mechanical room. As a result, surface testing for combustion residual was conducted on behalf of the building owner across various Phase II spaces, the utility connector and the distant mechanical room in an effort to characterize relative combustion particulate impact, if any, throughout these areas. In addition to serving as a basis for determining the scope of impacted areas and cleanup/remediation protocols, the raw data provided a bank of data by which to describe the behavior of soot loading (counts/mm2) and relative soot concentration (percent ratio; %R) as useful metrics within an appropriate inference model for quantifying differences in soot impact across a building.

2 Methods

2.1 Surface Sampling for Char and Soot

All surface samples were reported to have been collected from non-porous horizontal surfaces that had not been subjected to preliminary cleaning following smoke infiltration from the fire. Accordingly, specific sample location and number within a target zone were driven by visual indicators of impact, and included the ceiling plenum side of metal access panels, upper surfaces of metal light fixtures, shelving, and laboratory equipment. Sample collection was as per D6602 and the AIHA Wildfire Guide, using the Bio-Tape™ (Zefon International, Ocala, Florida). The Bio-Tape™ is a flexible plastic microscope slide with a standard adhesive area, providing more sampling consistency than the flexible/rolled “sticky tape” that requires more manipulation by an investigator. The Bio-Tape™ media were transmitted to an environmental laboratory experienced for analysis of settled combustion particulates via light microscopy.

For probabilistic evaluation purposes, three (3) major sampling zones for combustion particulate were identified, denoted as (1) Phase II, (2) Utility Tunnel, and (3) 2nd Floor Mechanical. The Phase II areas (adjacent to the Phase I “direct impact” zone) were comprised of smaller spaces identified as M, LN, LS and K + A. A schematic of the sampling zones is shown in Figure 1.

Figure 1
figure 1

Schematic of sampling zones

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Soot was reported for each sample as loading (soot count per square millimeter; Ct/mm2) and concentration (percent ratio; %R). The latter was determined by the proportion of soot aggregate particles counted relative to the total of other settled particles, as adjusted by the average particle size in each reporting category. The limit of detection (LOD) was reported as a calculated value based upon the number of combustion particulates (soot aggregates and char particles) counted within the area of the (sample) slide observed (microscope grid openings), as influenced by the background debris and particulate loading.

2.2 Data Analysis—Permutation/Randomization Based Inference on Δfd

Data from various zones were organized to construct potentially useful and informative comparisons around difference in frequency of detection (Δfd), under permutation/randomization (P/R) inference. In this analysis, the median of the combined (soot agglomerate) data from the particular two zone comparison was identified. If the data from the two zones are from the same distribution (i.e., represent the same degree of soot impact), by definition, there should not be a significant difference in the relative frequency of data points (Δfd) greater than the combined median. By extension, there should not be a significant Δfd relative to other values within the range of the combined data. Thus, the combined median, or alternatively the value resulting in the greatest Δfd, become a critical reference value (CRV) that serves to partition the combined data at the point representing the greatest difference for probabilistic comparison under the Δfd analysis model described herein. The probability (by which to infer quantitative/statistical significance) associated with Δfd in any data comparison can be calculated directly, the mechanics for which have been detailed previously for various environmental contaminants [40,41,42,43,44,45]. As an example, Table 1 displays the derivation (via direct calculation) of the probability associated with the occurrence of three (3) detections greater than the CRV in a nine (9) sample control zone (CZ), and five (5) detections in a seven (7) sample test zone (TZ). The frequency of detection (fd) for the combined data as specified under a null of no difference is 0.5 (calculated [3 + 5]/[9 + 7]); Δfd = 0.38095 (calculated [5/7] – [3/9]). The probability (p) for each possible fd in each zone is determined by appropriate substitutions in the axiomatic binomial random function (BRF). This is given by:

$$p =_{{\text{n}}} {\text{C}}_{{\text{x}}} ({\text{P}}^{{\text{x}}} )({\text{Q}}^{{{\text{n}} - {\text{x}}}} ),$$

where p = probability of x sample outcomes out of n samples detecting soot ≥ CRV, P = unbiased estimate (combining data from both zones) of soot fd ≥ CRV, Q = unbiased estimate of soot not being detected ≥ CRV; Q = 1 − P, n = total number of samples (in each zone), x = number of sample outcomes in which soot fd ≥ CRV, C = possible number of combinations of x outcomes in n samples detecting soot ≥ CRV; C = n!/[(n − x)!x!].

Table 1 Example of Randomization/Permutation Calculation of Total Probability for Data Exhibiting Δfd 0.38095 for n = 9 (CZ) and n = 7 (TZ) Sample Scheme
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For example, in the case of three (3) occurrences in the seven (7) sample TZ, p = 0.27344 calculated as (7!/3!*4!) × (0.5)3 × (0.5)4. The other occurrences (0/7, 1/7, etc. in the TZ and 0/9, 1/9, etc. in the CZ) similarly can be determined with the appropriate BRF substitutions. Examples of derivations for the CZ occurrences and the respective substitutions in the BRF are

$$\begin{aligned} & p\;{\text{for }}0/{9} = ({9}!/0!*{9}!) \times (0.5)^{0} \times (0.{5})^{{9}} = 0.00{195} \\ & p\;{\text{for 1}}/{9} = ({9}!/{1}!*{8}!) \times (0.5)^{{1}} \times (0.{5})^{{8}} = 0.0{1758} \\ & p\;{\text{for 2}}/{9} = {(9}!/{2}!*{7}!{)}*(0.5)^{{2}} \times (0.{5})^{{7}} = 0.0{7}0{31} \\ & {\text{etc}}. \\ \end{aligned}$$

Individual p values for occurrences in the CZ and TZ are indicated as the bolded values along the respective axes in the two-dimensional matrix of Table 1. The hypothesis tests the total probability (p) associated with the observed Δfd (in this case, all instances in which Δfd ≥ 0.38095), which is produced from the products of the underlying fds ≥ exhibited in the data. This is shown as the sum of the italicized/bolded values in the body of the matrix (rounded to 0.081).

The summed probability (p) is analogous to one tailed α in traditional negative hypothesis significance testing (NHST) following Neyman/Pearson (N/P) inference. It is applied for purposes herein within a conceptually parallel inferential framework to 1 − α to derive (in this case) 0.92. This is interpreted as 0.92 probability (rounded) that the test zone represents greater soot impact (“contamination”) than the control zone. The convention incorporated herein is pTZ > CZ (or pΔfd) = 0.92. In contrast, NHST and N/P inference, as the predominant (and frequently unchallenged) model within the public health/environmental, medical and engineering sciences, assumes validity of the mean in comparison of numerical contaminant (e.g., soot) “levels.” However, marked deviation from normally distributed surface contaminant data frequently encountered in post environmental “events” such as structural fires, establishes the potential for misleading inference (further shown herein) [28, 43, 46, 47]. To be noted is there is not necessarily a meaningful inferential difference between, for example, pΔfd = 0.92 as described here under P/R inference and the fixed decision criterion to reject the null of α = 0.05 as conventionally applied through traditional NHST to denote “significance.” As a result, P/R inference favors more flexibility in data assessment, based upon an investigator’s experience and understanding of the context and circumstances within which a particular evaluation and testing is conducted [3, 18, 42,43,44, 48, 49]. In this way, the probabilistic behavior of soot data presented as surface loading and concentration can be described and compared within the context of challenge/confirmation of hypotheses of differential impact of soot throughout a building or space.

3 Results and Discussion

3.1 Analytical Data

Individual soot data for the three (3) major test zones and the subzones within Phase II are shown for both surface loading (particle count; Ct/mm2) and size adjusted concentration (percent ratio; %R) in Table 2.

Table 2 Soot Surface Loading (Ct/mm2) and Concentration (Percent Ratio; %R) Data by Sampling Zone and Location
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3.2 Zone Comparisons—Surface Loading (Count/mm2)

Thirteen (13) different potential zone comparisons as might be utilized for soot loading (Ct/mm2) are displayed in Table 3. The CZ and TZ for each comparison (denoted as “Selection” in the last column) are identified as per the Phase II (to include the constituent subzones), Utility Connector, and 2nd Level Mechanical sampling zones. Mean values and standard deviation for surface loading are shown in the second and fourth columns respectively for reference (Selections 3/3A, 4/4A, 5/5A, 6/6A and 8/8A represent reverse comparisons by exchanging the data sets assigned as CZ and TZ as further discussed herein.)

Table 3 Zone Comparison Analysis Using Conventional N/P Inference Based on the Mean and P/R Inference on Δfd With Surface Loading (Ct/mm2) Metric for Soot
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The probability pΔfd under P/R is identified in the tenth column (“pTZ > CZ”) and is directly calculated relative to the CRV reference Ct/mm2, denoted “Ref” in the seventh column. (Italicized values in the tenth column indicate instances of consistent inference via P/R on Δfd for both soot count and soot concentration metrics across Tables 3 and 4.)

Table 4 Zone comparison analysis using conventional N/P inference based on the mean and P/R inference on Δfd with percent ratio (% Ratio) metric for soot
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Comparison of mean contaminant “levels,” which is represented under traditional NHST parametric statistical approaches by Student’s t, is shown in the fifth column. Mann–Whitney U (MW), a non parametric NHST equivalent of Student’s t based on difference in the mean of the ranked data, is identified in the sixth column. Probability values for both Student’s t and MW are displayed as 1 − α, which parallels the pTZ > TZ convention as described herein. This provides a useful context for the variation in inference regarding differences in the comparative soot data, recognizing the underlying probability (p) under NHST and P/R are derived under different assumptions and represent different phenomena [43, 50, 51].

For the soot count data, ten (10) of thirteen (13) comparisons (Selections) indicated a significant difference in soot loading in the designated test zone (TZ) through P/R inference with pΔfd ≥ 0.90. Of these, eight (8) comparisons (80%) as indicated by the bolded value in column pTZ>CZ, did not exhibit a significant difference via NHST using Student’s t or MW. Comparisons 4A and 5A were the only two selections in which a significant difference by either Student’s t or MW matched the P/R inference through pΔfd. Conversely, there were no instances in which a significant difference that was identified under traditional NHST was “missed” by Δfd (p < 0.90). Of particular note are the greater mean surface loadings in the designated CZ in Selections 4, 6 and 8A in which the identified TZ exhibited significantly greater soot impact via pΔfd. Thus, what appeared to be a “lower soot count” in the TZ amounted to a “false negative”.

Selections 4/4A, 6/6A and 8/8A are example data that clearly demonstrate the potential influence upon inference exerted by asymmetry in the comparative distributions, which has been recognized as a limitation for use of Student’s t [52]. Both zones in the respective reverse comparison exhibited greater soot impact via pΔfd, but at different CRV (reference) values. That is, the combined median in any given two zone comparison will be the same, regardless of whether the evaluation (generically) addresses “zone B” > “zone A” or “zone A” > “zone B”; thus the combined median serves as an initial “base” CRV value. However, the reference value generating the greatest Δfd may not always be the combined median (50th percentile). That is, the “CRVmax” may vary (occurring at a different percentile) depending upon which zone is designated the control zone (CZ) and which the test zone (TZ), as driven by the respective asymmetries in the comparative distributions. Thus, Selection 4A which produces pΔfd = 1.00 at a CRV of 22.8 Ct/mm2, identified LN + LS with greater soot (count) impact compared to the Utility Connector. The reverse comparison (Selection 4) indicated greater impact (pΔfd = 1.00) in the Utility Connector but at a CRV of 0.8 Ct//mm2. The same inferential analysis is used to identify greater soot impact in LS compared to K + A (Selection 6A; CRV = 9.6 Ct/mm2), and greater impact in LN + LS compared to K + A (Selection 8; CRV = 14.2 Ct/mm2).

3.3 Zone Comparisons – Soot Concentration (Percent Ratio)

The same thirteen (13) different zone comparisons as displayed in Table 3, are shown in the similarly constructed Table 4, using soot concentration (percent ratio; %R) as the metric.

For the percent ratio data, four (4) Selections (3, 4A, 5A and 8) indicated a significant difference in surface soot impact via pΔfd. Of these, only Selections 4A and 5A indicated a significant difference via Student’s t and MW (respectively), with conflicting inference between Student’s t and MW in Selection 5A.

3.4 Zone Comparisons—Combined Influence of Inference Model and Metric

Overall across the two metrics, to be noted is the frequent marked difference in inference regarding soot impact as indicated from pΔfd, and N/P under traditional NHST. Of the total twenty-six (26) combined comparisons for surface loading and concentration metrics, there were ten (10) occurrences of pΔfd ≥ 0.90 and four (4) occurrences of pΔfd ≥ 0.90 respectively. Of the fourteen (14) combined occurrences of pΔfd ≥ 0.90, parametric and non-parametric analysis under traditional NHST (Student’s t and MW) “missed” a significant difference using the generally applied α = 0.05 criterion in ten (10) instances. From an overall data evaluation perspective, the erratic performance of N/P inference using traditional parametric and non parametric NHST approaches also underscore the importance of assessing reverse comparisons in evaluating differential impact.

The potential for varying inference and resulting conclusions regarding impact as driven by the choice of soot metric is also clearly demonstrated. Comparison of the pΔfd generated by surface loading and concentration on the same soot data (same Selections across Tables 3 and 4 respectively) indicated agreement in seven (7) of thirteen (13) instances (italicized values in the tenth column, pTZ>TZ). This suggests an expected difference in conclusions regarding relative degrees of soot impact based on the metric utilized, of approximately fifty percent (50%). Moreover, surface loading appears to be a more consistent and discriminatory metric than concentration. That is, of the ten (10) instances of pΔfd ≥ 0.90 for surface loading data, only four (4) Selections (3, 4A, 5A, and 8) were matched via soot concentration. Conversely, all instances of a significant difference in concentration (%R) across comparative zones were similarly indicated by pΔfd ≥ 0.90 in the surface loading (Ct/mm2) data.

4 Summary and Conclusion

Tape sampling and analysis via light microscopy for combustion residual to include soot aggregates deposited on surfaces is frequently conducted to supplement visual inspection for post fire damage assessments in buildings. Light microscopy analysis provides identification of fire-related soot surface deposition, quantitatively expressed as either surface loading and/or concentration. While surface loading is an absolute metric for soot data, soot concentration as percent ratio is dependent upon the presence of other surface contaminants. In the absence of fixed numerical criteria for either metric, comparative sampling is necessary to identify (quantifiable/statistically based) differences in settled soot impact across comparative buildings or zones. The two interdependent components of the quantification problem inherent with comparative tape sampling/light microscopy data are (1) a standard soot metric utilized for comparison to a meaningful reference within (2) an appropriate statistical inference model. The fact that settled combustion particulate is considered a contaminant frequently drives the (faulty) assumption that tape sampling data represents (mean) mass of a target substance in the same sense as that of occupational/environmental exposure data. Under this paradigm, the N/P inference model through conventional NHST for comparative data analysis drives the heuristic use of numerical (mean) “levels” by either soot metric, which are not consistently useful in describing differences in zone impact as clearly shown herein.

It follows the data do not support the use of a universally fixed concentration (%R) as a criterion by which to consistently characterize suspect building spaces as contaminated with soot from any of the myriad potential background sources, let alone a specific fire. While a significant difference in absolute detection by either metric (pΔfd at CRV = 0) could theoretically quantify soot impact across building zones, the ubiquitous nature of soot as a potential constituent of background settled dust renders difference in absolute detection not consistently useful. However, aside from particle count or concentration metrics, differences in fd of a qualitative descriptor such as a characteristic wildfire source assemblage or unique “marker” can still be quantified via pΔfd, given P/R inference is based upon differences in distributional characteristics and not mean “levels” [23, 24, 31, 53].

For soot surface loading, laboratory standard operating procedures regarding for example, differentiation or combination of soot and char as a single reporting entity, and counting rules for individual vs. agglomerated particles will influence the nature of data. However, provided consistent sampling and laboratory analytical protocols are employed in a given circumstance, pΔfd avoids the statistical bias imposed by traditional NHST and N/P inference (e.g., comparison of “average soot levels”) with data that does not approximate normal [54]. To be noted is that the P/R inference model described herein is not influenced by ‘none detect’ data, and 0 values are utilized. That is, the common convention of substitution of arbitrary values (e.g., fraction of the analytical limits of detection) for none detect data is applicable for comparing data to a fixed numerical (frequently health based) standard. However, for sampling such as for post structural fires, substitution for none detect data potentially equalizes the data across comparative zones. More broadly, the lack of fixed numerical standards for settled soot data equates to the lack of a global reference distribution as required for analysis based upon the mean, and coupled with the erratic distribution of the data (e.g., marked deviation from normal), are violations of the fundamental assumptions for NHST [40, 51]. This is clearly reflected in the several instances of the failure of NHST to identify probabilistic differences in the soot data presented.

Finally, it follows that surface sampling that results in loss of the distributional nature of several individual/discrete samples for comparative zones, such as use of composite and/or wipe samples, does not allow for the appropriate quantitative inference. Ultimately the utility of post fire comparative surface sampling is as dependent upon the metric and inference model utilized as it is on the sampling and laboratory analytical protocols.